Question: Umaima is 18 years younger than Jessica. Jessica and Umaima first met 3 years ago. Eleven years ago, Jessica was 3 times older than Umaima. How old is Jessica now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Umaima. Let Jessica's current age be $j$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $j = u + 18$ Eleven years ago, Jessica was $j - 11$ years old, and Umaima was $u - 11$ years old. The information in the second sentence can be expressed in the following equation: $j - 11 = 3(u - 11)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = j - 18$ . Substituting this into our second equation, we get the equation: $j - 11 = 3($ $(j - 18)$ $ -$ $ 11)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 11 = 3j - 87$ Solving for $j$ , we get: $2 j = 76$ $j = 38$.